Problem: Solve for $x$ : $5\sqrt{x} - 3 = 8\sqrt{x} + 10$
Subtract $5\sqrt{x}$ from both sides: $(5\sqrt{x} - 3) - 5\sqrt{x} = (8\sqrt{x} + 10) - 5\sqrt{x}$ $-3 = 3\sqrt{x} + 10$ Subtract $10$ from both sides: $-3 - 10 = (3\sqrt{x} + 10) - 10$ $-13 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{-13}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $-\dfrac{13}{3} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.